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Mcalc : The Master Calculator. Registering Mcalc. ------------------ Mcalc is not "free", neither it is "public domain". It is a copyrighted and commercial program distributed through the shareware channel. This allows you to try the program first to see if it suits your needs. If you decide to continue using it after 3 weeks, then you are expected to pay the author a registration fee, which costs only 2000 Bef or $49 for individual use, or less per machine if you get a site license. Some users may even qualify for a free registration. All the features present in the registered version are also present in the evaluation copy. Only the extra add-in utilities have been removed from this copy as they could need too much disk spaces to be distribu- ted in a convenient way via the most used shareware channels: BBS and phone links. I think that by letting you try all of the features, you will decide to register if you want to continue using this program. Please, help prove me right be sending your registration. Your registration will motivate me to spend the time and resources necessary to add some of the features that you ask for. The delay screen at the end of this evaluation copy is not present in the registered version. Please, refer to the ORDER.DOC for instruction on how to register Mcalc, and prices. I will try to extend my support to unregistered users during their evaluation period, however, I reserve the right to limit my support for unregistered users if their requests become taxing for me. You may correspond by postal mail: please, send a self adressed stamped enveloped in order for me to reply. If your adress is outside Belgium, add a $1 money for the answer costs. Free registration for qualified students: if your school lab has a site license for the Master Calculator for use on 10 or more computers, then up to five students from your school can receive a free registered copy of the program. All you have to do is send me your request, along with thename of your school. Please, check first to make sure you qualify for this offer. A site is considered to be any corporation, institution, government agency, computer lab, or non-personal organization, with more than one computer capable of running Mcalc software, and with a locally accessible tech support person or team. A site may use the evaluation version for evaluation only. If the site decides to continue using Mcalc after 21 days, a site license must be purchased. See the ORDER.DOC for low rates that are available. A site license is for use within the site and is not transferable. 1 Mcalc : The Master Calculator. This license allows the internal use and copying of the sofware by as many computers as contracted for. The unregistered version may be freely distributed. The Master Calculator software is distributed on an "as is" basis without any warranty of any kind, expressed or implied. The author will not be liable for any special, incidental, consequential, direct or indirect damages due to any malfunctions. My adress: Didier Gosseau. Rue Georges Lorand nΦ 19. B 1050 Brussels. Belgium. Distribution: You are encouraged to distribute the shareware version of Mcalc. The following files must be present and unmodified: Mcalc.exe Master calculator task. Mcalc.hlp & Mcalc.hl2 On-line text and index files. mc_unit.dat Physical units database. Mcalc.key User key definition file. Helvb.fon Helveticca characters fonts. demo.bat demo.mac Demonstration macro and auxillary files. demo03a.mcp demo04.mcp demo05.txt mcalc.doc This file. order.doc The ordering form. The compressed file name must be MCALC19.??? with ??? being ARJ, ZIP or whatever compression suffix being used. 2 Mcalc : The Master Calculator. Contents. --------- 1. Introduction. 2. Mcalc features. 3. Installation. 4. Getting started. 5. Getting help with Mcalc. 6. A few first steps using Mcalc. 7. The Mcalc user interface in brief. 8. Functions and commands. 9. Procedures. 10. Using the plotter and the solver. 11. Using the statistical functions and commands. 12. Numerical analysis. 13. Physical units conversion. 14. Using the keyboard macros. 15. Advanced and particular topics. 16. The Mcalc files. 1. Introduction. ---------------- Mcalc is a scientific calculator for MSDOS based computers that offers a lot of features most of the time only available in high class scientific packages. Mcalc offers a lot of build in functions, operators, numerical notations and modes. Graphics, keyboard macros, user task extensions and many more are available. Expressions such as the following can be computed: 63 - 5 + 4.821 (5.9-abs(2.8/5-3))^2+sin(3-(pi+3/4) 15 * sin(pi/4)+abs(10-5+log(20)^2+9) - #b101110111 3 Mcalc : The Master Calculator. 2. Mcalc features. ------------------ - double precision 64 bits floating number calculation. - logical arithmetic syntax using a BASIC like recursive descent expression parser. - rich set of scientific functions including gaussian curve, bessel functions, statistical functions... - interactive functions, procedures and experimental data sets plotter. - rich set of commands including plotter, equation solver, integration, interpolation, multi-model regressions, correlation... - multiple programmer radix notation: decimal, hexadecimal, octal and binary. - programming possibilities via Procedure-Basic. - on-line hypertext help system. - physical units converter and intelligent units database. - customizable user keys. - keyboard macros. - extension possibilities via user "tasks". - session login file support - support CGA, EGA, VGA and coprocessor hardware on any AT, 386, 486 and PENTIUM platform. - needs MSDOS 3.3 or later. 3. Installation. ---------------- Make a \mcalc subdirectory into your harddisk and copy all the files to it. All files beginning with "demo**.***" constitutes a demonstration tutorial of Mcalc possibilities. They are not necessary for commun use and can be deleted if you don't plan to run the demonstration. Mcalc must be run from its current directory. 4. Getting started. ------------------- There are three ways to run Mcalc: - from the command line: mcalc 5+4*8/2 4 Mcalc : The Master Calculator. - in evaluation mode: mcalc [enter] when you are in this mode, you get the mcalc> prompt that invites you to enter a mcalc command or an expression to be evaluated. In this mode, strike [F1] at any time for help, or [Alt-F10] to quit the program. See the examples later in this documentation to get more ideas about using Mcalc. - in procedure mode. You can evaluate a procedure from within Mcalc. The best way to evaluate Mcalc is first to run the demonstration tutorial. To do that, make sure that you are in the Mcalc subdirectory and that the following files are available: - mcalc.exe, mcalc.hlp and mcalc.hl2 - helvb.fon, mcalc.key and mc_unit.dat - demo.bat, demo03a.mcp, demo04.mcp and demo05.txt From the DOS, give the following command: DEMO.BAT The demonstration tutorial is started. Don't strike any key during the demonstration, excepted when the <<<Demo is pausing>>> label is displayed. The compleet demonstration takes approximately 20 minutes. After the demo, you will have a good idea about Mcalc possibilities. If something goes wrong or you want to abort the demo, strike one or more time the [Ctrl End] key. Then, at the mcalc> prompt, type the 'quit' command, followed by [Enter]. After the demo, continue the evaluation Mcalc by yourself. You should look at the on-line help system if you need detailled information about a particular topics. This documentation is just intended to help you starting with Mcalc. Each time you should learn more detailled info, we will direct you to a particular help topic. 5. Getting help with Mcalc. --------------------------- Inside Mcalc, you can obtain help at any time, by striking [F1] in response to the Mcalc> prompt. You can also get help, by entering the 'help' command followed by return. You can finally obtain help about a particular subject by entering the 'help' command, followed by the subject between double quotes. For example, to obtain help about the on-line help system, strike: help "???" 5 Mcalc : The Master Calculator. 6. A few first steps using Mcalc. --------------------------------- The first time you use Mcalc, you will get the following screen: Mcalc, the Master Calculator. Version : 1.99 Copyright (C) 1994 by Didier Gosseau. Give 'help' or strike F1 for help, 'listk' or Ctrl F1 for function keys. 'mcalc.ini' not found! Default values will be used... Use the 'setup' command to customize them. Mcalc > This is normal. Mcalc uses default values that are customized. It store them into the 'mcalc.ini' file. At the first usage, that file does not already exists. Mcalc created it and give you a warning. We will ignore that message for now, and performs a few using the default parameters.When you get the "mcalc >" prompt, this means that Mcalc is ready and wait for a command or an expression to compute. 6.1.Evaluating a simple expression. ----------------------------------- Mcalc is now ready to evaluate a simple expression. Let suppose you want to compute the following: 12.4 * 5 / 4 You just strike this expression, as you would normally write it on a paper, and Mcalc supplied immediately the answer: mcalc > 12.4*5/4 Answer = 15.5 mcalc > As you see, each time you strike an expression, it is directly evaluated using the standard arithmetic notation. Later in this manual, we will explain in details the rules used to write correctly an expression. 6 Mcalc : The Master Calculator. 6.2. Evaluating a complex expression. ------------------------------------- Mcalc is also directly suitable to evaluate a more complicated expression, involving number and constants. For example, let us try to find the value of a second order polynomial: ax^2 + bx + c where a=1, b=-2 and c=-3. Let suppose x=-5. You could for example directly strike: mcalc > 1*(-5)^2-2*(-5)-3 Answer = 32 but it is also possible to use variables to store constant values.... mcalc > a=1 mcalc > b=-2 mcalc > c=-3 mcalc > x=-5 mcalc > +a*x^2+b*x+c Answer = 32 6.3. Writing a simple procedure to plot this polynomial. -------------------------------------------------------- If you have to evaluate this polynomial for multiple values of x, it is preferable to write this equation as a simple procedure. For example, you can write directly the equation: y = ax^2 + bx + c as a procedure that can be evaluated or plotted later. To do that, you give the edit command, that enter the edit mode. Then, you strike e to select the (E)dit option of the displayed menu. You are now in the Internal editor. Despite its very limited features, it is enough for today to enter this one line equation. You strike now directly the equation, just like you would have written it on a paper! Strike: y=a*x^2+b*x+c followed by a Return. The first and unique line of this small procedure is written. You strike now ESCape to quit the internal editor. If you want, you can save the procedure as a file for later usage. To do that, strike s to select the (S)ave function. Mcalc prompt 7 Mcalc : The Master Calculator. you for a file name. Enter for example: ex1 followed by Return. Your screen looks now like the following: y=a*x^2+b*x+c Command mode : (L)oad, (S)ave, (E)dit, (R)un, (N)ew, (D)ir ,(Q)uit You have now written a procedure that compute an expression that is function of the variables a,b,c and x and that returns a value into the variable y. In our case, a,b and c are constants and their values are already stored. We don't need to enter them again. As long as you stay within Mcalc, the values assigned to variables are not lost. We have thus a procedure that is a function of variable x and that send back an answer in variable y. Strike now q to (Q)uit the editor mode. You get back the mcalc> prompt. You can now plot the function using the plot command. To plot a procedure, you just need to specify the independent or input variable name (in our case 'x'), the dependant or output variable (here 'y'), the first and last values of the input variable, and the number of points to plot. In this example, we plot 100 points for x in the range [-5,10]. mcalc > plot x,y,-5,10,100 You are now in interactive mode. This mode give you some possibilities that will be explained in great details in chapter 5. For now, just look at the graphic and note that the function has two roots at approximately -1.5 and +3.5. It is now interesting to use the solver to find the exact values of these roots. 6.4. Using the solver. ---------------------- To use the solver, you write a procedure exactly on the same manner as you do to plot a function. In this example, the procedure EX1 is already loaded and ready for use. You find a root using the solve command. You must also specify the independent or input variable name, the output variable and an initial root value to start the solver. In this example, we start searching a root from -1.5. 8 Mcalc : The Master Calculator. mcalc > solve x,y,-1.5 Solving the procedure ..... Solver root/extremum found: Root = -1.00000009449577 [ -1.5 ] Eval = 3.7798309193704e-007 Another case ? = <Y> Initial approximation [ -1e+050,1e+050 ] = 3.5 Solving the procedure ..... Solver root/extremum found: Root = 3.00000009763274 [ 3.5 ] Eval = 3.90530948024548e-007 Another case ? = <N> mcalc > As you can see, Mcalc has found a first root at -1 and a second one at +3. This was of course the expected results for such quadratic polynomial.... 7. The Mcalc user interface in brief. ------------------------------------- 7.1. Evaluation and procedure modes. ------------------------------------ Mcalc uses two working modes: evaluation and procedure. When you start Mcalc, you get the 'mcalc >' prompt. This means that you are in evaluation mode. Each time you enter one line and press Return, Mcalc evaluate the line you typed and look to compute the expression, or to recognize a command and execute it. In this mode, Mcalc can only recognize three basic situations: An expression is available. In this case, Mcalc evaluate it and returns the value with the 'answer' prompt. mcalc > *12*sin(45)+exp(-1)*fact(5) Answer = 52.630814314811640 Mcalc can evaluate many expressions in one step. Multiple expressions must be separated by "space" characters. 9 Mcalc : The Master Calculator. mcalc > 12/3 4*5 (4+2)/0.1 Answer = 4 Answer = 20 Answer = 60 The second case is a variable assignment. In this case, you assign the value of an expression to a variable, like in the following example: mcalc > a=sin(45)/3 The expression (in this example: sin(45)/3 ) is evaluated and the resulting value is stored into the specified variable ('a' in this case!). The last case, a command is given and will be processed.... mcalc > cls In this example, the 'cls' keyword is recognized and will be executed. It clears the screen's contents. 7.2. The notation used. ----------------------- Mcalc use a notation for the functions, commands and expressions that is very similar to BASIC. This is the reason that we have called the procedure language the Procedure Basic. You should only keep in mind that normally any expression is supposed to be in decimal. Other radix numbers can be entered using a particular prefix. The '#' sign introduces another radix than decimal. Mcalc recognizes the following prefix: #x #h #o #b #a and #v. For more info: help "notation" 7.3. Specifying default parameters with 'setup'. ------------------------------------------------ In practice, Mcalc does not ask you every time if arc expressions are entered in degree or radian, if a mouse must be used in graphical mode , and so on. Mcalc based its behaviour on default parameters that you can modify using the 'setup' command. When the command is given, Mcalc starts a dialogue where is displays each current settings. You can modify a setting by entering another value. 10 Mcalc : The Master Calculator. If you strike just a Return, you means that you agree with the proposed value and don't want to modify it. If you strike just a /, you means that you agree with the proposed value, don't want to modify it, nor any further question. Giving a slash ('/') in a Mcalc dialogue means that you want to stop that dialogue! When you quit Mcalc, your current settings are saved into a file 'mcalc.ini'. The next time you start Mcalc, the settings are directly loaded from that file and available. The first time you use Mcalc, default settings values are used because the 'mcalc.ini' file does not exist! For more info: help "setup" 7.4. User defined keys. ----------------------- The functions keys F1 to F10 and their associated keys, Shift, Control and Alternate are called user defined keys. When you install Mcalc, some strings are associated to some of these keys. If you give the liskk command, Mcalc replies with the list of all user defined keys that have some string attached to them. For more info: help "listk" 7.5. Last result and last commands. ----------------------------------- When in evaluation mode, Mcalc always remember the last answer and store it internally. The 'last' keyword is used as an expression returning the last calculation answer. By that way, it is very easy to split a long calculus into smaller one, without having to retype the answer. For example, suppose you have to compute the following expressions: 12/(45-32) 12/(45-32) + 1/8 As you can see, the second expression will be the same as the first one, but having 1/8 added. You do this easily with Mcalc using the following sequence: 11 Mcalc : The Master Calculator. mcalc > 12/(45-32) Answer = 0.923076923076923 mcalc > last+1/8 Answer = 1.048076923076923 mcalc > For more info: help "last" Another useful features of Mcalc evaluation mode is the ability to retrieve previous expression to modify them. Mcalc remembers the 20 last expressions or commands you have used in evaluation mode. By striking the Up arrow, you display the previous expression from the buffer. By striking the Down arrow, you retrieve the next expression. If you have executed correctly this tutorial worked example, by following carefully the steps described in this documentation, if now you strike once the Up key, you get the following: mcalc > last+1/8 If you strike immediately return, the same expression is evaluate again. Do it now. mcalc > last+1/8 Answer = 1.173076923076923 mcalc > As you can see, you don't obtain the same result, because with such kind of expression, each type you evaluate it, the next last result is stored into the 'last' variable! Suppose now that you have to evaluate the following expression: 12/(45-32) + 1/6 The quickest way to do it is to retrieve the previous expression that look the most like this one. Strike the Up key until you see the following on your screen: mcalc > 12/(45-32) Now, strike 10 times the Right key until the cursor is just after the closing ). An other manner is to strike the End key, that moves the cursor at the end of the line. Now, fill the remainder of the expression: +1/6 and strike a return. You obtain: 12 Mcalc : The Master Calculator. mcalc > 12/(45-32)+1/6 Answer = 1.089743589743590 Please, remember that in evaluation mode, the Up and Down keys display the previous or next expressions from the list of the last 20 previously evaluated expressions or commands. The End and Home keys move the cursor at the end or the beginning of the current line. The Enter or Return keys start the evaluation of the expression, or command. If the key is not at the beginning or the end of the line, everything at the right of the cursor is ignored. 7.6. Changing the output format. -------------------------------- Mcalc offers you the possibilities to modify the output number presentation. To do that, you use the format command. By default, Mcalc displays numbers in floating notation using 15 digits after the dot. You may modify this in accordance with your own needs using the following syntax: format "format string" The format is defined using the language C ANSI format specifiers. For more info: help "format" 7.7. Evaluating an expression and respecting priorities. -------------------------------------------------------- The kernel of Mcalc is a piece of software called the parser. The parser, or expression parser, transforms numeric expressions into a form that the computer can understand and evaluate. In Mcalc, we use a recursive descent parser. This complicate name means that any expression is decomposed into simplest one, that are also decomposed and this process occurs until the expression is reduced to a single value. Despite the fact that this looks very complicated to explain in details, it is exactly the same as what you do implicitly when you try to solve an expression like: 9/3 - (100 + 56) When you compute such expression, first you recognize that this expression is composed of two terms: 9/3 and (100+56).You break the expression into a sum (or difference) of terms. 13 Mcalc : The Master Calculator. Next, for each term, you break it into a product of factor. (The product can be a multiplication of a division.) In this case, the first term 9/3 is composed of the two factors 9 and 3. Next, each factor can be a variable, a number or an expression. If it is an expression, the same process must be repeated reccursively: breaking into terms and factors and subexpression. In this example, the factors 9 and 3 being the simplest numbers, the term 9/3 = 3 can be evaluate. The second term (100 + 56) must now be evaluate. We break it into terms 100 and 56. Each term is broken into factors: here very obvious : 100 and 56. The second term is evaluate and is 156. Now the expression is reduced to two terms : 3 - 156. They are broken into terms: 3 and 156. These terms are obvious and cannot be split into factor. They are thus directly evaluated and we obtain finally : -153. As you can see from this process, Mcalc will naturally follows some precedence of operators when parsing an expression. From the highest to the lowest priorities, it recognizes: functions ( ) ^ means 'power of' 2^3 = 2 * 2 * 2 * / multiplication & division + - sum and difference This means that the following expressions are equivalent: 9/3 + 100 + 56 (9/3) + (100+56) Because / is executed before +, an expression like (9/3)+ is the same as 9/3+ . Also, (100 + 56) will be computed before +100 + 56, but the result is the same! But, you must use parenthesis if you assign more priorities to the sum than for the product, because in such case you don't respect Mcalc parser rules. For example: 14 Mcalc : The Master Calculator. (9+3) / (4+5) is not the same as: 9+3 / 4+5 Don't forget that Mcalc ignores the tabulations and spaces in an expression. 7.8. Using variables. --------------------- Mcalc provides 26 direct access variables named 'a' to 'z'. You can use them to store temporary values or constants very often used, or during a procedure. Mcalc also supplies up to 8000 indirect access variables. The number of available variables depends of your memory and the setup. For more info: help "variables" For more info: help "setup" For more info: help "list" 8. Functions and commands. -------------------------- The Mcalc's parser recognizes some keywords. These keywords are linked to a particular meaning. Each keyword can be a function, a command or a separator. A function evaluate an expression and returns an unique value. That value can be displayed or used inside a more complex expression. The function takes expects eventually a list of other expression enclosed into (). Some expression expects no argument and return a value, like 'pi'. Other expects one or more arguments as 'sin(arc)'. A command is a special keyword that expects eventually some extra arguments using a particular syntax. It initiates an action. The action can display a result, but does not returns a value. In other words, a function can be enclosed into an expression, while a command may expect one or more expressions as arguments, but cannot be enclosed itself into another expression. For more info: help "keywords" For more info: help "functions" For more info: help "commands" 15 Mcalc : The Master Calculator. 9. Procedures. -------------- 9.1. Purpose and limitations of "Procedure-Basic". -------------------------------------------------- The Procedure-Basic language is the programming language used by Mcalc. Some commands are used in evaluation mode, like for example format, edit, list ... but most of the commands are used in procedure running mode. Up to now, we have always used Mcalc as a simple calculator. This means that expressions and commands were directly processed from the command line. This is the evaluation mode. It is also possible to write a series of instructions into a file called a program or a procedure. Then you run the compleat procedure after. This delayed mode is called the procedure mode. The language used to write such procedures is called Procedure-Basic because it is a BASIC like language. Procedure-Basic is intended to write procedures, not programs. Mcalc being a calculator and not a BASIC interpreter, we consider a procedure as a small program only intended to describe easily some equations or to perform simple tasks. Due to this specific and limited purpose, Procedure-Basic is a small subset of BASIC, but includes powerful commands like solve, plot ... Also a procedure is subject to the following limitations: - no string character variables and operators. - only one instruction or expression by line. - maximum 50 lines / procedure. - incorporated editor works only with the 20 first lines of a procedure. You should not consider Procedure-Basic as a traditional programming language to write sophisticated programs. It is only intended to write single tasks or medium complexity expressions. 9.2. The Procedure-Basic instructions set. ------------------------------------------ We only introduce here the various keywords of Procedure-Basic. Please, refer to the on-line help for detailed explanations about each keyword. The language recognizes the following: The input and print commands are used to perform input/output with the user. 'input' is used to temporary stop the program, let the user enter a value which is assigned to a variable. The 'print' command is used to display string message and expression's values. 16 Mcalc : The Master Calculator. Specific input/output operations from/to text files are possible using read, read_, write, close, finput, finput_ and print. These permits reading values from a file, processing them with Mcalc and writing results back to another file. The if...then and goto commands are used to control the execution flow conditionally and unconditionally. The gosub and return keywords are used to redirect the execution flow to/from subroutine. Up to 20 levels of subroutines may be cascaded. A subroutine is useful to perform continuously the same task, without having to rewrite it at many place in the procedure. You can also use run to chain a procedure to another one. The for...to...step and next keywords are used to perform loop operation. Finally graph,pixel, dot and line are used for procedure controlled graphics. The end keyword is used to finish a procedure execution. For more info: help "procedure_basic" 9.3. Writing a simple procedure. -------------------------------- Let suppose you have very often to convert distance from km to miles. It could be useful to write a simple procedure that ask you to enter a distance in km and that convert it into mile. The conversion result is displayed and the execution finish. Such a procedure is trivial and could be: input "Enter km to convert : ",k print "Equivalent in mile : "; k / 1.609344 end To edit and save such procedure, from the Mcalc prompt, give the edit command. Strike now a e to (E)dit the procedure. Enter the three lines and finish each with a enter. Strike the <ESC> key to return to menu. Select now option (S)ave and save this procedure under the name 'mile'. The screen looks now as this one : 17 Mcalc : The Master Calculator. input "Enter km to convert : ",k print "Equivalent in miles : ";k / 1.609344 end Command mode : (L)oad, (S)ave, (E)dit, (R)un, (N)ew, (D)ir, (Q)uit The procedure is ready to run. Run it by striking the (R)un option. You obtain the following screen if you answer for example 10 at the question. Enter km to convert : 10 Equivalent in miles : 6.213711922373339 Mcalc > To execute a second case, strike the F2 key or type edit and strike r again. Answer another value. If you have to convert many values, it is preferable that the program is modified like this one: 10 input "Enter km to convert (negative value to quit) : ",k if k < 0 then end print "Equivalent in mile : "; k / 1.609344 goto 10 To modify the program, select again F2 or edit, then the (E)dit option. Now you have to retype completely the first line. (The small incorporate editor does not support character insertion.) Finish the line with a enter. This will automatically insert an empty line for the second line of our procedure. Now type the line 'if k<0 then end' but don't strike any Enter at the end of this line. Move now the cursor to the beginning of the fourth line and overwrite the 'end' with 'goto 10'. Strike an <ESC> to quit the edition mode. Select (R)un. Because you have modified the procedure, Mcalc ask you if you want to save it. Answer 'Y' for Yes and return. The previous file is overwritten by the new one, and the execution is started.... Enter km to convert (negative value to quit) : 1 Equivalent in miles : 0.621371192237334 Enter km to convert (negative value to quit) : 10 Equivalent in miles : 6.2137119223733900 Enter km to convert (negative value to quit) : 100 Equivalent in miles : 62.1371192237339000 Enter km to convert (negative value to quit) : 2 Equivalent in miles : 1.242742384474668 Enter km to convert (negative value to quit) : -1 18 Mcalc : The Master Calculator. Mcalc > For more info: help "edit" For more info: help "internal_editor" 9.4. Running a procedure. ------------------------- To execute a procedure, you have the following possibilities: 1. Go in editor mode with edit. Load the procedure to the editor memory with (L)oad. or Write the procedure with (E)dit. Select the (R)un option. 2. If the procedure is already in the editor memory.... Strike F2 followed by R. 3. You can also directly load a procedure from a file and run it with the run command. For example: quit Mcalc, restart it and give directly the command: run 'mile' Mcalc > run "mile" Enter km to convert (negative value to quit) : 12 Equivalent in miles : 7.4564543068980070 Enter km to convert (negative value to quit) : -1 Mcalc > 4. If a procedure begins with a label (the address of a goto statement for example) and is already loaded into memory, you can run it with the run command followed by that label. For example, our 'mile' procedure begins with the label '10'. You can run it again by giving: Mcalc > run 10 Enter km to convert (negative value to quit) : 2 Equivalent in miles : 1.242742384474668 Enter km to convert (negative value to quit) : -1 Mcalc > For more info: help "run" 19 Mcalc : The Master Calculator. 9.5. Multiple entries procedure and function keys. -------------------------------------------------- With Mcalc, you can write multiple entries procedure and call each subprocedure using its label or a function key. For example, write the following procedure and save it under the name 'convert'. 1 input "km-->mile : ",k print k;" km = "; k/1.609344 ; "mile" end 2 input "mile-->km : ",k print k;" mile = "; k*1.609344 ; "km" end Now, be sure that this procedure is loaded into the editor memory. (To be sure, give the edit command: the procedure must be displayed). If it is not the case load it. Quit the editor mode and come back into the evaluation mode. To convert a km distance into miles, type run 1. To make the inverse conversion, type run 2. Mcalc > run 1 km-->mile : 2 2.000000000000000 km = 1.242742384474668 mile Mcalc > run 2 mile-->km : 1.242742384474668 1.242742384474668 mile = 2.000000000000000 km Mcalc > A very useful feature of Mcalc is the user function keys to run a procedure. If you strike a SHIFT Function key, automatically it runs the procedure from the label 0 to 9. (Label 0 is affected to Shift F10, label 1 to Shift F1 ....). For example, to convert now a km into mile, strike Shift F1. To convert mile to km, strike Shift F2. 20 Mcalc : The Master Calculator. 9.6. Debugging a procedure. --------------------------- If you suspect some fault into a procedure, it is possible to debug it. To debug a procedure, Mcalc supplies two features selectable via the setup command: Procedure break enabled. = When you run a procedure very long (or mayby error an infinite loop), if you strike any key and this flag is set, the running procedure is aborted. If this flag is reset, the keystroke is ignored. Default mode is 'Yes'. Procedure trace mode enabled. = When this flag is set and a procedure is running, it will run in single step mode. Default mode is 'No'. Give now the setup command and modify this last flag to 'Y'. Finish with a '/' to avoid listing all other settings. Now, Mcalc reacts strangely with the following: Mcalc > setup General purpose flags: Trigonometric mode : (R)adian, (D)egree = <D> Programmer binary output. = <N> Help automatically supplied. = <N> Procedure break enabled. = <Y> Procedure trace mode enabled. = <Y> Display status in prompt = </> k := 0.000000000000000 ---> 2.000000000000000 Next instruction : end Strike any key to continue ..., <ESC> to abort! Strike a <ESC> and you obtain the Mcalc prompt again. When the procedure trace mode is enabled, Mcalc displays each instruction before executing it. Also, each time the content of any variable 'a' to 'z' is modified, Mcalc displays the previous and the new values. You have to strike a key to proceed with the instruction. If you strike <ESC>, you cancel the procedure execution and come back to the prompt. For example, strike the Shift F1 key to convert 12 km into miles.... 21 Mcalc : The Master Calculator. Mcalc > run 1 km-->mile : 12 k := 2.000000000000000 ---> 12.000000000000000 Next instruction : Strike any key to continue ..., <ESC> to abort! Strike now any key, excepted <ESC>. Mcalc continues and execute the print command... 12.000000000000000 km = 19.312128000000000 mile Next instruction : end Strike any key to continue ..., <ESC> to abort! Mcalc > Give again the setup command and switch back the 'trace' flag to 'N'. Keep the 'Procedure break enabled' active. Now, write this stupid infinite loop procedure and save it as a file under the name 'bug'. i=1 10 print i i=i+1 goto 10 end Now, run it. You will see the loop is continuously restarted and you loose the control of Mcalc. If such occurs, it is always possible to break a running procedure by striking any key when the procedure is running. This is only possible if the 'Procedure break enabled' flag from setup is 'Y'. Else, your key strokes are ignored and you have to restart your computer to keep the control back. If the 'Procedure break enabled' is set to 'N', the speed of running procedure is slightly increased. Use only this setting to run safe procedure, already debugged, and when you experience that it runs slowly !!! 22 Mcalc : The Master Calculator. 9.7. Using an external editor. ------------------------------ The internal editor provided by Mcalc is small and fast, but very limited in its features. This is not a major limitation of Mcalc as it is possible to configure it to use your favourite editor. To use another editor, called an external editor because it is not part of Mcalc, you need to define one MSDOS environment variable. The procedure is fully described into the registered version user manual of Mcalc. Remark: The registered version of Mcalc is supplied now with its own editor: Notepad.Exe. It is strongly advised to use this editor, as it includes special features suitable for using when editing a keyboard macro. 10. Using the plotter and the root solver. ------------------------------------------ With Mcalc, you can plot easily any equation, or user defined function. You can also find the root of such equation. You will find the description and an example in the online help. For more info: help "plot" For more info: help "solve" For more info: help "solve_" If you want to plot an expression that is not directly writable in the form of a function y=f(x), such as a parametric equation, you can write a procedure using the 'graph' command and related commands. For more info: help "graph" For example, the following procedure can be used to draw a lissajou figure: 23 Mcalc : The Master Calculator. 1 print "Lissajou figure...." print " " input "Enter frequency 1 : ",a input "Enter frequency 2 : ",b input "Number of points : ",n d = 2 * pi / n graph -1.2,-1.2,3.2,1.2 t=0 for i=0 to n step 1 x=2.0 * cos(a*t) + 1.0 y=sin(b*t) if i=0 then pixel x,y,-1 line x,y t=t+d next end 11. Using the statistical functions and commands. ------------------------------------------------- Mcalc supplies the following commands and functions. The read_ command is used to read a data structured file into the memory variables. When the data are loaded, further statistical process are possibles. The mean and sigma functions are available to compute the average and the standard spread over a serie of numbers. The cor command can be used to compute a correlation function between two series of values. The reg command lets you compute very sophisticated statistics. These regression results can be viewed as data tables using listr or as graphics via plotr. Also, Mcalc supplies two functions to study gaussian normal distribution: normal and inormal. For more info: help "statistics" 11.1. Reading a structured data file. ------------------------------------- A structured data file is a text file that contains columns of values. The demonstration file "demo05.txt" is a good example of structured data file. As you can see if you type or print it, this file contains a serie of columns of values. The first line is a text that play a role of comment for us. To load for example the data relative at a linear function, let us give the following command: 24 Mcalc : The Master Calculator. R_Mcalc > read_ "demo05",2,10,1,2 File loaded! Area pointer is at #26. R_Mcalc > For more info: help "read_" Mcalc responds is the value of an 'Area Pointer'. 11.2. The concept of area pointer. ---------------------------------- Most statistical process, such as regression analysis or statistical calculations are done on large series of numbers. It is thus necessary to use a convenient notation to specify a serie of numbers quickly and easily. This is the purpose of the Area Pointer concept used by Mcalc. An area pointer is a block of successive contiguous memories (direct or indirect access) whose contents give the adress of other indirect access memories. For more info: help "area_pointer" The following figure illustrate the concept of Area Pointer: Area_Pointer │ │ │ │ Contiguous block: └─────>── Area_X────────────────>──Contiguous block Area_Y────────────────>──Contiguous block Area_Z────────────────>──Contiguous block Area_R────────────────>──Contiguous block Area_Size As you can see on this figure, an Area Pointer is just a succession of 5 variables. The first four contain a value that is a pointer to a variable block. Each pointer is the indirect access adress of the first variable of each block. The fith value is the size of the first three blocks. An area pointer is refered by its starting adress. This means the indirect adress of the first pointer to the first X block. Each block is contiguous; this means that inside a block all variables are used. The concept of Area Pointer is powerfull enougth to works with blocks that are not necessary contiguous with each other. This is not the case in our previous example, but could be so. 25 Mcalc : The Master Calculator. Summary: Each time you load a data serie from a data structured file using the read_ command, Mcalc returns you the adress of an Area Pointer. This unique adress will be used to specify your data during each regression calculus. 11.3. Computing single statistics. ---------------------------------- When your data are loaded into memory, you can use the mean and sigma functions to perform statistical calculations. In our previous example, we have loaded two series of numbers representing the x and y values for 10 points. Let us now compute the mean and average of x series.... For more info: help "mean" See also related topics: sigma, min and max. R_Mcalc > mean(40,10) Answer = 16.75 R_Mcalc > sigma(40,10) Answer = 4.54147553114624 11.4. Performing linear and non-linear regression analysis. ----------------------------------------------------------- A linear regression analysis can be computed directly using the reg command. The command uses the following syntax: reg area pointer , 0 , order In fact, Mcalc performs a polynomial regresssion. Order is the degree of the polynome. By specifing a order=1, you obtain a linear regression. Compute the linear regression from the already loaded data of the previous example: R_Mcalc > reg 26,0,1 Regression in progress! Please wait .... Regression results: Coef[00]= 3 Coef[01]= 2 Regression sigma = 0 Correlation = 1 R_Mcalc > For more info: help "reg" For more info: help "plotr" For more info: help "listr" 26 Mcalc : The Master Calculator. 11.5. Manual regression using the solver. ----------------------------------------- Despite the fact that the Mcalc user defined model offers already a lot of possibilities, there are situations where the equation cannot be defined with any of the previous model. In such situation, it is still possible to perform a regression using a least square criterium model, via a combination of a Procedure, the solver and an iteration algorithm. You will find a full chapter dedicated to this subject, with worked examples, in the manual supplied with the registered version of Mcalc. 12. Numerical analysis. ----------------------- Mcalc supplies also special commands used for numerical analysis. For more info: help "integral" For more info: help "interpol" This shareware package is supplied with the procedure "demo04.mcp" that can be used to draw an interpolated curve going through a serie of data points loaded via 'read_' or computed and stored in memory by any other method. Refer also to the demonstration to see directly that procedure at work. 13. Physical units conversion. ------------------------------ Mcalc is supplied with a database of up to around 100 units. Via the 'convert', 'rconv' and 'iconv' commands, you can convert values between units. For more info: help "convert" The registered version of Mcalc is supplied with an utility that can be used to customize the database following your needs. A database have space for up to 200 units! 27 Mcalc : The Master Calculator. 14. Using keyboard macros. -------------------------- Mcalc supports keyboard macros. A macro is just a sequence of keystrokes that can be played automatically after you have stored them into a file. The compleet demonstration used in this package has been implementated as an unique macro. For more info: help "macro" The macro compiler and the description of how to write and run macros are described in details in the registered version of Mcalc. 15. Advanced and particular topics. ----------------------------------- 15.1. Session log file support. ------------------------------- If you use a small desk calculator, you are sometimes happy having a paper roll printout of al the operations you perform. By that way, if you discover a mistake after a long series of operations, you can always look at the paper to find your error or to remember how you did some specific calculations. A similar facility is available with Mcalc and is called the log file. A log file is a text file where all the dialog from the main screen can be redirected. To use the log file system, you just use two commands: write and close. The write command is used to specify the loggin file you want the listing of your current session to go. You may get the loggin on any ASCII text file, or on the line printer. For example, to make a log file 'mylog.txt' of the current session, give the following command: D_Mcalc > write "mylog.txt" D_Mcalc > Now, all the dialog you type and Mcalc answers go to that file. This is true, as well in evaluation mode, as all 'print' instructions in procedure mode. The log file is appended until: - you use another 'write' command. - you close the logger with the 'close' command. - you quit Mcalc with the 'quit' command. 28 Mcalc : The Master Calculator. If the specified log file already exists, it is appended; it is never overwritten. Please, refer to the on-line help for the compleat syntax of the 'write' command. In the log file, your input commands (in evaluation mode) are always preceded by a ';' character. Mcalc answers looks exactly as they come on the screen. The debugging information in trace mode, or the iterations of the solver are not copied to the log file. 15.2. The initialization 'mcalc.mcp' procedure. ----------------------------------------------- When you start Mcalc, it search in the working directory for a procedure named 'Mcalc'. If it find it, it will run it automatically( a little bit as the 'autoexec.bat' file of your PC). By that way, you have the possibility to initialize some variables or to open always a log file, or thinks like that. You must take care of two things, when you create this procedure: - it must always finish with the 'end' instruction. - it may not include instructions like 'setup' that initiate a dialog (or you have to answer the dialog before the procedure will continue). This is true for any kind of procedure. Tips: The 'mcalc' procedure can be very useful if you plan to work always with the same ten user functions Shift_F1 to Shift_F10. In such case, write a procedure with multiple entries as described in chapter 4. Preceded the first label by a line with 'end' or the initialization procedure finished by 'end'. So, each time you start Mcalc, the initialization is done and your keystroke procedures are available. Another way to work is to create one simple initialisation procedure that contains and finish with a 'load' instruction, such that your favourite procedure is directly available when you start Mcalc. 29 Mcalc : The Master Calculator. 15.3. Using the command line mode. ---------------------------------- The command line mode is a special case of the evaluation mode. If you have only one calculation to do, it is possible to specify the expression directly into the command line, at the same time you type 'mcalc' to start Mcalc. For example, from the DOS prompt, type the following to make this calculation: C:\TOOLS>mcalc sqrt(1-cos(30)^2) Answer = 0.5 C:\TOOLS> If the expression you type at the command prompt could interfere with MSDOS, enclose it within quotes.... C:\C\SOURCE>mcalc 12/5 Answer = 2.4 C:\C\SOURCE>mcalc 12 / 5 Answer = 12 C:\C\SOURCE>mcalc "12 / 5" Answer = 2.4 C:\C\SOURCE> In the first case, Mcalc recognizes a correct expression, because '12/5' was in one word. In the second case, Mcalc make a mistake because MSDOS interprets ' 12 / 5 ' as three different words, and Mcalc expects only one expression in the command line. The third example is correct, because MSDOS recognizes this time the whole expression between quotes as one unique word. 15.4. Using graphical fonts files. ---------------------------------- When in graphical mode, Mcalc can use character fonts to improve the graphic quality. A graphic font is a file having a .FON extension, like the one delivered with Windows 3.1. This package is delivered with the file HELVB.FON that contains Helvetica fonts you can use if you have an EGA or VGA adapter. To use this font file with a EGA or VGA adapter, and assuming you have copied all Mcalc files into the subdirectory c:\mcalc, you must give the two commands before starting Mcalc: 30 Mcalc : The Master Calculator. set fontdir=c:\mcalc set fontface=t'helv'w10h8b You could for example add these two commands into your autoexec.bat file. Before using fonts, you must also enable their usage via the 'setup' command. For more info: help "setup" 15.5. Customizing user function keys. ------------------------------------- The Mcalc package is supplied with the mcalc.key file. This file contains the definition assigned to the function keys F1 to F10, Shift, Ctrl & Alt, inside Mcalc. To view the current assignment of these keys, give the listk command. The registered version of Mcalc is distributed with the two files: mckey.lst and mckey.exe. With these two files, you have the possibility to modify the user key definitions as you want. For more info: help "mckey" 31 Mcalc : The Master Calculator. 16. The Mcalc files. -------------------- Version 1.99 of Mcalc uses and recognizes the following files: mcalc.exe is the Mcalc program itself. mcalc.hlp & mcalc.hl2 are the online help files. The first contains all the help material, while the second supplies the fast access index system. mcalc.ini is the file that store your current setup. It is created the first time you run Mcalc. mcalc.lic is the license information file for registered users. helvb.fon is the Helveticca fonts characters to use in graphic mode. .mcp all Master Calculator Procedures are text files having that extension. .mem all variables dump files produced with 'savevar'. mc_unit.dat the database of physical units. mcalc.key the user keys definition file (compiled). mckey.lst the user keys definition file (source). mckey.exe utility to make mcalc.key. makeunit.exe utility to edit mc_unit.dat. notepad.* the supplied editor. assist.exe the assistant add-in. mac.exe & mcmac.exe the macro compiler and its driver. Remark: Not all these files are supplied with the shareware version! 32